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Volumn 81, Issue 6, 2010, Pages

Schelling segregation in an open city: A kinetically constrained Blume-Emery-Griffiths spin-1 system

Author keywords

[No Author keywords available]

Indexed keywords

CORUNDUM; DYNAMICS; STATISTICAL PHYSICS;

EID: 77953990479     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.066120     Document Type: Article
Times cited : (46)

References (27)
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    • The only exception is a study with a nonfixed fraction of agents of each type, where the Schelling model is simply replaced by the Ising model: this corresponds to a situation with no vacancies and with moves consisting in replacing an agent of a given type by an agent of the other type
    • The only exception is a study with a nonfixed fraction of agents of each type, where the Schelling model is simply replaced by the Ising model: this corresponds to a situation with no vacancies and with moves consisting in replacing an agent of a given type by an agent of the other type.
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    • The proof is left to the reader. One shows that the considered dynamics is a Monte Carlo dynamics for a BEG model at the temperature 1/β, with a transition matrix which is irreducible and satisfies the detailed-balance condition. If q± is the fraction of agents of type ±1 in the reservoir, for any nonzero rate of exchanges with the reservoir one gets as stationary state the Gibbs distribution associated to the energy EBEG (K=2T-1,2D ) - 1 2β [ln ( q+ q- ) i ci2 +ln q+ q- i ci ]. In the present case q± =1/2
    • The proof is left to the reader. One shows that the considered dynamics is a Monte Carlo dynamics for a BEG model at the temperature 1 / β, with a transition matrix which is irreducible and satisfies the detailed-balance condition. If q ± is the fraction of agents of type ± 1 in the reservoir, for any nonzero rate of exchanges with the reservoir one gets as stationary state the Gibbs distribution associated to the energy E B E G (K = 2 T - 1, 2 D) - 1 2 β [ln (q + q -) i c i 2 + ln q + q - i c i]. In the present case q ± = 1 / 2.


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